SOLUTION: the sum of the digits of a two digit number is 12. if the digits are reversed the number is 15 more than twice the orignal number what is the original number? how did you get it?

Question 128076: the sum of the digits of a two digit number is 12. if the digits are reversed the number is 15 more than twice the orignal number what is the original number? how did you get it?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the sum of the digits of a two digit number is 12. if the digits are reversed the number is 15 more than twice the orignal number what is the original number? how did you get it?
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Let the number be 10t+u where t is the ten's digit and u is the unit's digit.
------------------------
Equations:
Sum of the digits is 12:
t+u = 12
If digits are reversed etc.
10u+t = 2(10t+u) + 15
---------------
Rearrange the equations:
t+u = 12
19t - 8u = -15
----------------------
Solve the 1st for "t":
t = 12-u
Substitute in the 2nd to solve for "u":
19(12-u)-8u = -15
228 - 27u = -15
27u = 243
u = 9 (the unit's digit of the original number)
t = 12-u
t = 12-9 = 3 (the ten's digit of the original number)
=================
The original number is 39
==========================
Cheers,
Stan H.
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